A length is measured as 15.0 m with an uncertainty of ±0.5 m. If this length is
Practice Questions
Q1
A length is measured as 15.0 m with an uncertainty of ±0.5 m. If this length is used to calculate the area of a rectangle, what is the maximum possible error in the area calculation?
15 m²
7.5 m²
3.75 m²
1.5 m²
Questions & Step-by-Step Solutions
A length is measured as 15.0 m with an uncertainty of ±0.5 m. If this length is used to calculate the area of a rectangle, what is the maximum possible error in the area calculation?
Step 1: Understand that the length of the rectangle is given as 15.0 m.
Step 2: Note that there is an uncertainty in the length measurement, which is ±0.5 m.
Step 3: Recognize that the area of a rectangle is calculated using the formula: Area = length × width.
Step 4: Since we are only given one length and no width, we will assume the width is also the same as the length for this calculation.
Step 5: Calculate the maximum possible error in the area using the formula: Maximum error in area = 2 × length × uncertainty.
Step 6: Substitute the values into the formula: Maximum error in area = 2 × 15.0 m × 0.5 m.
Step 7: Perform the multiplication: 2 × 15.0 = 30.0 and then 30.0 × 0.5 = 15.0.
Step 8: Conclude that the maximum possible error in the area calculation is 15 m².
Measurement Uncertainty – Understanding how uncertainty in measurements affects calculated values, particularly in area calculations.
Area Calculation – Applying the formula for the area of a rectangle and understanding how to incorporate uncertainties in the dimensions.
Propagation of Uncertainty – Using the correct method to propagate uncertainties when performing calculations involving multiple variables.
